if a man in an elevator drops his briefcase but it does not fall to the floor what can you conclude about the elevator's motion
 

Dear Student,

If briefcase does not fall, the acceleration of briefcase with respect to man(or elevator) is zero. So elevator is also under free fall condition and moving down with the acceleration of 'g'.

One more possibility, if elevator is falling with more acceleration than 'g'. In this case, acceleration of briefcase with respect to man(or elevator) will be towards ceiling. And,  briefcase will not touch floor but will touch ceiling. 

Regards,

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